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INFLUENCE OF HEEL ON YACHT SAILPLAN PERFORMANCE Fabio Fossati, Full Professor, Wind Tunnel - Politecnico di Milano, Italy, fabio.fossati@polimi.it Sara Muggiasca, Researcher, Department of Mechanical Engineering, Politecnico di Milano, Italy SUMMARY This paper presents research activities carried out by the authors to investigate the influence of heel on yacht sailplan performance by means of wind tunnel test techniques and CFD numerical simulations. Main results concerning wind tunnel testing activities carried out in the Politecnico di Milano Twisted Flow Wind Tunnel investigating the upwind performance of sails both heeled and upright are presented. Finally the heeled plane approach which is largely used in the aerodynamic models available up to-date for VPP use is outlined and discussed . 1. INTRODUCTION available up to-date for VPP use is outlined and discussed. Sailing yacht heeling effect on sails aerodynamics represents one of the tougher issue of upwind 2. TWISTED FLOW WIND TUNNEL aerodynamics ([1] [3] [6] [7]) and some discussions have been recently found in literature] [8]. In fact this is a very With the purpose of supporting, with a state of the art complex topic with strong implications for facility, the world-wide recognised excellence of methodologies to compute sailboat aerodynamics for Politecnico di Milano research in the field Wind Velocity Prediction Program design tool. Engineering as well as general Aerodynamics, This paper deals with research activities carried out at Politecnico di Milano decided to design and build a new Politecnico di Milano Twisted Flow Wind Tunnel in large wind tunnel having a very wide spectrum of order to investigate the performance of upwind sails in applications and very high standards of flow quality and heeled condition. This work is a part of an overall and testing facilities. The Wind Tunnel has been fully comprehensive general research program started in 2005 operative since September 2001 and from the first year of with partial funding from the ORC with the aim to operations has been booked for sailing yacht design investigate a series of rig planform variations in mainsail applications. roach and jib overlap in order to overcome some Figure 1 shows an overview of the P.d.M. facility: it’s a perceived inequities in the ratings of boats of various rig closed circuit facility in a vertical arrangement having design racing under the International Measurement two test sections, a 4 x 4m high speed low turbulence and System (IMS). a 14 x 4m low speed boundary layer test section. The results of this investigation are used to assist the A peculiarity of the facility is the presence of two test International Technical Committee (ITC) in changing the sections of very different characteristics, offering a very formulations in the ORC INTERNATIONAL VPP sail wide spectrum of flow conditions, from very low aerodynamic model. turbulence and high speed in the contracted 4 x 4m This paper in the first part presents test arrangements, section (Iu<0.15%, Vmax=55 m/s), to earth boundary procedures and methodologies that have been carried out layer simulation in the large wind engineering test both for systematic gathering of wind tunnel data and section. subsequent analysis in order to describe aerodynamic With reference to yacht sails aerodynamic studies, they behaviour of different sailplans both in upright and are performed in the boundary layer test section which heeled condition. Some interesting experimental results allows for testing large scale models (typically 1:10 -1:12 and trends are presented and discussed. for IACC yacht model) with low blockage effects at Differences of sail performance at different heel maximum speed of 15 m/s. configurations outlined by means of wind tunnel test A very important peculiarity concerning yacht results are clarified with the aid of numerical results aerodynamics is that since the wind speed increases with obtained using RANS methods performed on the tested height due to the boundary layer phenomena and the boat sailplan configurations. For this reason, during the tests speed is constant, this means that the apparent wind authors gave special attention to measure also sails flying speed incident onto a yacht also increases with height shapes in order to provide sails geometry useful for CFD and, in addition, its direction changes, rotating away purposes. from the yacht’s heading with increased height. Paper presents also a detailed description of methods and This is a very important topic in wind tunnel testing on techniques used by the authors in order to detect sails sailing yacht scale models, that has to be carefully shapes. considered, because the forces developed by the sail plan Finally the so called “heeled plane approach” [3], [6], [7] are due to the apparent wind incident onto the sails and which is largely used in the aerodynamic models 11 the sail shape and trim is strongly related to the apparent techniques, the model can be rigged using standard wind profile. model yacht fittings and small dinghy fittings without Therefore, for proper similitude modelling, the apparent any additional work becoming too small to handle, wind velocity shear and twist profile has to be commercially available model yacht sheet winches can reproduced in the wind tunnel for testing stationary be used and, most important, deck layout can be models. reproduced around the sheet winch, allowing all the sails to be trimmed as in real life. Figure 1. Politecnico di Milano Wind Tunnel While the variation in wind speed with height can be modelled in the wind tunnel using similar procedures as Figure 2. Twisted Flow Devices for conventional wind engineering testing, the twisted Moreover the model yacht drum type sheets are operated flow is a more difficult task to deal with for a stationary through a 7 channel proportional radio control system, wind tunnel yacht model, because the true and apparent except that the aerial is replaced by a hard wire link and wind speeds are coincident. the usual joystick transmitter is replaced by a console At this purpose the so called Twisted Vanes Device has with a 7 multi-turn control knobs that allow winch drum been designed: the basic idea of the design process is to positions to be recorded and re-established if necessary. generate a large-scale vortex with its spin axis aligned The sheet trims are controlled by the sail trimmer who with the wind tunnel steady state flow direction, resulting operates from the wind tunnel control room. in a twisted flow area corresponding to the model Figs. 3 show a typical model mounted in the wind tunnel. location. Moreover, basic design requests were the following: • easy to adjust • easy to install/remove • economical solution both in terms of first installation and running costs The originality of the Politecnico di Milano Twisted Flow Device compared to the other solutions [4] is the central positioning of the device, not occupying the entire tunnel section. In fact, the role of the Twisted Flow Figure 3. Yacht model in the boundary layer test section Device is just to turn left the lower part and to turn right the upper part of the flow. The side flow not passing A high performance strain gage dynamic conditioning though the vanes is allowed to move vertically balancing system is used for balance signal conditioning purposes. the flow rate. The balance is placed inside the yacht hull in such a way Fig. 2 shows the Twisted Flow Device in the tunnel that X axis is always aligned with the yacht longitudinal boundary test section. axis while the model can be heeled with respect to the A complete model, consisting of yacht hull body (above balance. the waterline) with deck, mast, rigging and sails is The wind tunnel is operated at a constant speed after the mounted on a six component balance, which is fitted on wind speed profile and wind twist have been properly the turntable of the wind tunnel (fig. 5). The turntable is tuned considering the desired targets, which are automatically operated from the control room enabling a previously calculated considering the potential boat 360° range of headings. performance at different true wind speeds and yacht courses. As previously said the velocity profile can be 3.1 Test arrangements and measurements setup simulated by means of independent control of the The large size of the low speed test section enables yacht rotation speed of each fan joined to the traditional spires models of quite large size to be used, so that the sails are & roughness technique, while the twist can be simulated large enough to be made using normal sail making by twisting the flexible vanes by different amounts over 12 the height range. The wind tunnel speed is most usually The photogrammetry based technique is relatively fast limited by the strength of the model mast and rigging and during the tunnel occupancy phase and in principle it the power of the sheet winches. requires only three digital images be recorded from Data acquisition can be performed in several ways: the useful points. In order to overcome difficulties arising usual procedure provides direct digital data acquisition from sails overlapping especially in downwind by means of National Instruments Data Acquisition configurations and in order to be able to have at least Boards (from 12 to 16 bits, from 8 differential channels three useful points in each part of the sails the system is up to 64 single-ended) and suitably written programs equipped with eight cameras. For the present tests this according to Matlab standards. system is composed of five cameras, filming reflective The data acquisition software calculates the forces and targets placed on sails in sync, and a PC equipped with moments using the dynamometer calibration matrix. The acquiring and processing custom-made software. forces are shown in the virtual panel designed on the Cameras have resolution of 1392 x 1040 pixels, computer screen in real time so that the sail trim can be greyscale 1/2” CCD sensor, 17 fps (frames per second). optimised because the effects of trimming the sails on the Each of them mounts an optical zoom and a high driving and heeling forces can be directly appreciated. intensity infrared (830 nm) LED illuminator, triggered to The model is set at an apparent wind angle and at a fixed simultaneously flash with cameras frame rate. In order to heel. After a sail trim has been explored, actual reduce at the best cameras vibrations induced by the measurements are obtained by sampling the data over a wind, it was decided to fix cameras on photographic period specified by the test manager (generally 30 heads constrained to the available stiffest points in the seconds) with a sample frequency specified too. An wind tunnel (fig.6). important feature of wind testing procedure is that the model should be easily visible during the tests so that the sail tell-tales can be seen by the sail trimmer. For this purposes some cameras placed in the wind tunnel as well as onboard allow a view similar to the real life situation (fig.4). Figure 4. Wind tunnel top and deck camera view during testing Figure 6. Yacht model and cameras in the wind tunnel High reflective markers are glued on 8 horizontal In order to correlate force measurement readings and the sections of each sail plus one on the top, on both sail shape and in order to provide input data for CFD windward and leeward side (fig 7). calculations, an in-house photogrammetric measuring system has been developed to recover flying shapes during tests (fig.5). Figure 7. Reflective markers on the main Then, a custom-made software performs real time blob detection and stores images sourced from cameras on a hard disk. Figure 5. Flying shape measurement system layout 13 As a result of this routine a table with the 2D blob heeling angle, heeling force has to be reduced by the detected coordinates is available for post process. crew. The sail trimming routine adopted was to choose the mainsail traveller position (initially quite high up to windward) and then to vary the incidence and the twist of the mainsail to power or de-power it, by over-trimming or easing the main traveller and main sheet. The genoa was initially trimmed in order to have the maximum driving force condition and was fixed varying the mainsail shape. Once a specific trimming condition is obtained using the real time force and moments values displayed by the data acquisition system, a 30 seconds acquisition sampling has been performed with 100Hz sample frequency, and both time histories and mean values of each measured quantity have been stored in a file. The usual way of analysing data is to compare non dimensional coefficients, allowing to compare the efficiency of sails of different total area at different conditions of dynamic pressure. The first analysis performed is the variation of driving force coefficient Cx with heeling force coefficient Cy. They are given by the expressions: Fx Cx = 1 2 Sv 2 Fy Cy = Figure 8. Sails flying shape detection process 1 2 Sv 2 (1) Cameras have been previously calibrated using a custom where built calibration frame. • Fx is the driving force The 3D marker points coordinate for each sail are then • Fy is the heeling force obtained by means of a DLT (Direct Linear • S is the actual sail area Transformation) algorithm, reaching marker position • V is the wind speed with an uncertainty equal to 0,5 mm. • is air density Marker coordinates are obtained as mean of their position over a 20[sec] acquisition period with 17 Hz As an example fig. 9 shows a comparative plot of Cx acquisition rate. versus Cy for the apparent wind angles tested. Each run Then this 3D points array are used for surface modelling (with its corresponding measured values) is shown for as well as to extract the trim parameters as explained in each AWA. [5]. 3.2 Upwind sails testing procedure For each apparent wind angle tested the first task was to reach the maximum driving force potentially achievable. At the same time it was observed the influence of the sails trimming changes using the data acquisition program that visualizes the forces acting on yacht model in real time. Trimming the sails to obtain optimum sailing points proved to be the most challenging task of the testing process. Attempts were made to carry out the job as systematically as possible. Firstly, the maximum drive point was found by trimming the sails to the best using Figure 9: Driving force coefficient vs heeling force the cameras views, the tufts on the sails and the force coefficient measurements output data. It can be seen that there are some sails settings at the From there, the heeling force would be reduced to highest values of heeling force coefficients where the simulate the trim of the sails for windier conditions. In driving force is lower than the maximum value. These fact in real life windy conditions, to keep the optimum non optimum values were obtained by oversheeting the 14 sails such that the mainsail generally had a tight leech and the airflow separated in the head of the sail. Therefore a selection was made to choose those points that formed the envelope curves (maximum Cx for a given Cy value) for each apparent wind angle (fig. 9). Envelope curves have been drawn through the test points with the greatest driving force at a given heeling force. An example is reported in fig. 10. Figure 11. Centre of effort height vs heeling force coefficient Figure 10. Driving force coefficient envelope vs heeling force coefficient For the purpose of the analysis, in the following only these points will be used. The centre of effort height, Ceh, is obtained by dividing the roll moment by the heeling force component in the yacht body reference system: Mx Ceh = Fy As an example, a plot of its variation with heeling force Figure 12. Centre of effort longitudinal position vs heeling for all angles can be seen in fig 11. Both all the measured force coefficient values and the envelope of the points corresponding to maximum driving force at each heeling force are reported. The results are given in terms of ratio between 3. SAILPLANS TESTED centre of effort height from boat deck and mast height According to the overall activities program 3 different (P+BAS). The centre of effort longitudinal position, Cea, main sails (with the same actual area but 3 different is obtained by dividing the yaw moment by the heeling roaches) named Mims, Mhr, and Mtri and 3 different jibs force component in the yacht body reference system: with different overlap (named G100, G135 and G150) Mz have been combined in a 92% fractionality Cea = configuration.. Note that the Mims mainsail has the IMS Fy maximum allowed roach without any penalty applied As an example, a plot of its variation with heeling force according to the IMS rule. for all angles can be seen in fig 12. Both all the measured Mainsail Roach level has been defined according to: values and the envelope of the points corresponding to IMS maximum driving force at each heeling force are AreaMain reported. Cea is measured from the origin of the balance Roach = 1 (positive to bow) which is placed behind the mast. P*E / 2 (2) The results are given in terms of ratio between centre of Mainsails codes and dimensions are defined as follows: effort longitudinal position from balance origin and yacht model waterline length. Roach P E It can be seen that Cea moves forward as Cy reduces. Mims 0.193 1.94 0.637 This is explained by the way the sails are de-powered. Mhr 0.335 1.94 0.571 Mtri 0.096 1.94 0.695 Tab. 1 15 Jib codes are defined as follows: Overlap G100 100% G135 135% G150 150% Tab. 2 All configurations were tested in upright condition and at 30° heeling too. Only the IMS mainsail+135% jib have been tested at 15° heeled condition too. Table 3 summarises the situation. Upright Heel 15° Heel 30° Mims G100 X X Mims G135 X X X Mims G150 X X Mhr G100 X X Mtri G100 X X Tab. 3 Figures 13-17 show the different sailplans during the tests. Figure 14. MtriG100 sailplan Figure 15. MimsG100 sailplan Apparent wind angles were chosen to be 22°, 27°, 32° and 42° which cover the upwind range. For each apparent wind angle, sail trimming during the wind tunnel tests were performed according to the abovementioned procedure. All the sails trimming have been performed by Gigio Russo of North Sails Italia Figure 13. MhrG100 sailplan using the remote control console for model winches. At the same time it was observed the influence of the sails trimming changes using the data acquisition program that visualizes the forces acting on yacht model in real time. 16 • Mx is the heeling moment • S is the actual sail area • Hmast is the mast height from the deck • Va is apparent wind speed • is air density The apparent wind speed Va and apparent wind angle are evaluated in the heeled plane perpendicular to the mast according to: ( ) + (Vt sin ) 2 2 Va = Vt cos cos (4) V sin cos AWA = arctg t Vt cos where represent the true wind angle (yaw angle), Vt is the wind tunnel flow velocity corresponding to the mean dynamic pressure at each run and is the heel angle. Figures 18-21 show test results relevant to the mainsail medium roach and medium overlapping jib (MimsG135) sailplan in terms of envelope curves (maximum Cx for a given Cmx value) for each apparent wind angle. In particular in each figure results are reported with reference to each apparent wind angle tested in upright and heeled condition too: in this case the resulting apparent wind angle according to eqn. 4 is shown in the Figure 16. MimsG150 salplan legend. 0.35 AWA 19.3 MimsG135 AWA 21.3 MimsG135 AWA 22 MimsG135 0.3 0.25 Cx [-] 0.2 0.15 0.1 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 CMx [-] Figure 18. MimsG135 sailplan Figure 17. MimsG135 sailplan 0.5 AWA 23.8 MimsG135 4. EXPERIMENTAL RESULTS 0.45 AWA 26.2 MimsG135 AWA 27 MimsG135 Using the aerodynamic driving force and aerodynamic heeling moment Fx and CMx component in the yacht 0.4 body reference system the corresponding coefficients have been obtained as follows: Cx [-] 0.35 Fx Cx = 1 0.3 SVa2 (3) 2 Mx 0.25 CM x = 1 SH mastVa2 0.2 2 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 CMx [-] where • Fx is the driving force Figure 19. MimsG135 sailplan 17 0.65 0.5 AWA 28.4 MimsG135 AWA 23.8 MhrG100 0.6 AWA 31.1 MimsG135 AWA 27 MhrG100 0.45 AWA 32 MimsG135 0.55 0.4 0.5 0.35 Cx [-] Cx [-] 0.45 0.3 0.4 0.25 0.35 0.3 0.2 0.25 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 CMx [-] CMx [-] Figure 20. MimsG135 sailplan Figure 23. MhrG100 sailplan 0.9 0.65 AWA 28.4 MhrG100 AWA 37.9 MimsG135 0.6 AWA 32 MhrG100 0.8 AWA 41 MimsG135 AWA 42 MimsG135 0.55 0.7 0.5 0.6 0.45 Cx [-] Cx [-] 0.5 0.4 0.35 0.4 0.3 0.3 0.25 0.2 0.2 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 CMx [-] CMx [-] Figure 21. MimsG135 sailplan Figure 24. MhrG100 sailplan As can be seen the effect of heel is to reduce the 0.75 maximum driving force produced by sails at each AWA 37.9 MhrG100 apparent wind angle tested and this effect increases with 0.7 AWA 42 MhrG100 the heeling angle increasing. 0.65 The same situation has been found for each sailplan 0.6 tested: as an example figures 22-25 refer to max roach mainsail with non overlapping jib (MhrG100). 0.55 Cx [-] 0.45 0.5 AWA 19.3 MhrG100 0.45 0.4 AWA 22 MhrG100 0.4 0.35 0.35 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 Cx [-] CMx [-] 0.25 Figure 25. MhrG100 sailplan 0.2 Another interesting feature is that the reduction in 0.15 driving force is more evident in fully powered condition than in the depowered ones and this is a general trend for 0.1 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 each sailplan tested. CMx [-] With reference to the mainsail medium roach and medium overlapping jib (MimsG135) sailplan figure 26 Figure 22. MhrG100 sailplan shows the ratio between the driving force coefficient at different heel angle and the same quantity in upright condition for each apparent wind angle relevant to the 18 sailplan trim allowing for the maximum driving force. carried out and put in the numerical model of the wind These ratio can be interpreted as a sort of efficiency tunnel (figure 32). The boundary conditions were set to parameter of the sailplan heeled condition. give a wind velocity profile similar to that in the wind tunnel. Mims G135 Mims G150 1.05 1.2 1 0.95 0.9 awa 22 1 awa 22 cx ratio cx ratio 0.85 awa 27 awa 27 0.8 awa 32 awa 32 0.75 awa 42 0.8 awa 42 0.7 0.65 0.6 0.6 0 10 20 30 40 0 10 20 30 40 heel [deg] heel [deg] Figure 26. MimsG135 sailplan Figure 29. MimsG150 sailplan Figure 27 is relevant to heeling force coefficient ratio of Mhr G100 the same (MimsG135) sailplan. 1.2 MimsG135 1 awa 22 1.05 cx ratio awa 27 1 awa 32 0.95 0.8 awa 42 0.9 awa 22 cy ratio 0.85 awa 27 0.8 awa 32 0.6 0.75 awa 42 0 10 20 30 40 0.7 heel [deg] 0.65 0.6 0 10 20 30 40 Figure 30. MhrG100 sailplan heel [deg] Mtri G100 Figure 27. MimsG135 sailplan 1.2 All the performed tests revealed a decrease in sailplan driving force when the sailplan heels (figures 28-31). 1 awa 22 cx ratio awa 27 awa 32 Mims G100 0.8 awa 42 1.2 0.6 awa 22 0 10 20 30 40 1 cx ratio awa 27 heel [deg] awa 32 0.8 awa 42 Figure 31. MtriG100 sailplan 0.6 0 10 20 30 40 heel [deg] Figure 28. MimsG100 sailplan In order to gain further understanding of the sailplans aerodynamic behaviour experimentally outlined numerical simulations have been carried out using RANS methods. In particular numerical simulations have been performed by means of FLUENT CFD code with the realizable k- turbulence model. A numerical model of each tested sailplan including hull and rigging has been Figure 32. Wind tunnel and yacht numerical model 19 In the following, for lack of space, results concerning on the sailplan windward side; moreover in the lower only the medium roach mainsail with non overlapping jib part of the jib pressure increases with heel reducing the (MimsG100) will be reported. suction on the leeward side. Fig. 33 shows numerical model of sails including yacht In order to understand this behaviour it’s useful to refer hull, which has been used to simulate yacht upwind to figures 41-42 which show the flow velocity vectors behaviour at different heel angles (sailing upright, coloured by magnitude (normalised to the free stream 15°heeled and 30° heeled) . incoming flow) in a plane perpendicular to the mast at Numerical simulation have been performed at 22° 25% of mast height from the deck respectively for apparent wind angle and for each of the heel angle upright, 15°heeled and 30° heeled conditions. considered the flying shape corresponding to maximum drive condition trimming at different heel angle has been used in order to generate the numerical mesh. Figure 35. Leeward Cp contours at 15° heel Figure 33. MimsG100 sailplan numerical model Figures 34-35-36 show the MimsG100 sailplan leeward side pressure coefficient contour respectively for upright, 15°heeled and 30° heeled condition concerning 22° apparent wind angle close hauled sailing condition analysis. Figure 36. Leeward Cp contours at 30° heel Figure 31. Leeward Cp contours in upright condition As can be seen heel increasing result in a less of a Figure 37. Windward Cp contours in upright condition pressure drop on both the sails, due to pressure decrease 20 stated by the heeled plane model described in the next paragraph. Figure 38. Windward Cp contours at 15° heel Figure 41. Velocity vectors in a plane perpendicular to the mast (25% mast height ) at 15° heel Figure 39. Windward Cp contours at 30° heel When the yacht heels flow angle of attack reduces and the corresponding lift decreases, leading to a reduction of the driving force too. As can be seen upright condition is associated to some separation on the jib leeward side which disappears at higher heel angles, leading to a lift Figure 42. Velocity vectors in a plane perpendicular to the reduction too. mast (25% mast height ) at 30° heel 5. AERO MODELLING AND HEELED PLANE APPROACH: SOME CONSIDERATIONS Since 1978 when the first velocity prediction programs for yachts was officially introduced for rating purposes the problem of modelling sail forces is a fundamental focus. With reference to most of up to date available VPPs it can be said that aerodynamic model is mainly derived from the first aerodynamic model well known as Kerwin model [3]. Many principles of the aerodynamics of sails can be taken from the thin airfoil theory even if significant differences can be found: in a similar way to a wing Figure 40. Velocity vectors in a plane perpendicular to the yacht sails are lifting bodies where due to their shapes mast (25% mast height ) in upright condition and the direction of the onset flow circulation appears increasing fluid velocity on the leeward side and This flow behaviour around the sails confirms also the decreasing velocity in the windward side with a apparent wind angle reduction associated to heeling as 21 consequent high pressure region on the windward side In particular for each test performed (as indicated on the and low-pressure region on the leeward side. abscissa axis named “prove” in fig. 44) the 3 component The lift and drag forces, resulting from the pressure of the aerodynamic measured force are reported. regions around the sails can be expressed in terms of Zloc non-dimensional coefficients so that any forces and moments can be evaluated considering actual sail area and dynamic pressure of the free stream onset speed of the flow. With reference to a wing the lift and drag coefficients are primarily a function of the angle of attack: on a sailing Xloc = Xbil yacht this quantity is not easy to be defined due to continuous sails shape changing due to sails trimming. Yloc Hence in case of sails the angle of attack concept is replaced by the apparent wind angle which is the angle Ybil between the relative free-stream onset flow and the yacht centreline. Zbil Moreover the free-stream speed of the onset flow to be used in evaluate the dynamic pressure is usually Figure 43. Balance and boat reference systems considered to be the apparent wind speed. With reference to fig. 44 blue symbols are relevant to Wind tunnel tests and full scale experiments are the most balance axes aerodynamic force components (named suitable way to evaluate the drag and lift coefficients of “bil”) while red symbols are relevant to the boat the sailplan for different apparent wind angles reference system values (named “loc”) defined in fig. 43. considering the sails geometry, the relative direction of More in details in figure 44: the onset flow, the flow structure (gradient and twist) and the trim of the sails. • Runs 1-16 are 22° AWA and 30° heel tests A typical representation of forces acting on the sailplan • Runs 17-28 are 27° AWA and 30° heel tests are based on lift and drag sailplan coefficients plotted against the apparent wind angle. • Runs 29-42 are 32° AWA and 30° heel tests The effect of heel is generally taken into account using • Runs 43-62 are 22° AWA and 30° heel tests the so called effective angle theory [Jackson, Campbell] • Runs 63-95 are 42° AWA and upright tests which is used to address the fact that the heel angle • Runs 96-109 are 32° AWA and upright tests influences the flow around the sails since the onset flow • Runs 110-122 are 27° AWA and upright tests can always been considered as being horizontal. As the • Runs 123-136 are 22° AWA and upright tests yacht heels the onset flow is not longer perpendicular to the leading edge of the sails and due this the resulting lift As can be seen the aerodynamic force component along and drag forces are different for each heel angle. the mast (“zloc” component) is quite zero except for the Each aero model must take into account for the fact that 42°AWA runs: this was a systematic effects shown by lift and drag coefficients are no only a function of the tests with each sailplan tested. apparent wind angle but also of the yacht heel. Kerwin [3] and the so called effective angle theory assume that the sails are insensitive to the flow component along their span (i.e. along the mast) and that only the flow component perpendicular to the mast produces the lift and drag forces. This represents one of the tougher issue of upwind aerodynamics and some discussions have been found in literature also very recently [Jackson 2001], [Teeters Sea Horse]. Aim of this paragraph is to discuss the appropriateness of this assumption and to investigate in more details its consequences on results available from aero models based on this underlying hypothesis. More in details the flow component along the chord of the sails can be seen as the flow component in the heeled plane, which is a plane perpendicular to the mast and this means that the sails are insensitive to the flow component Figure 44. MimsG100 runs sequence along the mast. Experimental measures demonstrate that Kerwin As an example in fig. 44 all tests performed by the assumption that the sails are insensitive to the flow authors for MimsG100 sail plan are reported (136 runs). component along the mast is substantially verified. 22 Coming back to the “heeled plane” model, the flow component in the heeled plane is called the effective flow and is defined by the effective angle and effective speed according to the following equations: ( ) + (Vt sin ) 2 2 Va = Vt cos cos (5) V sin cos AWA = arctg t Vt cos where represent the true wind angle (yaw angle), Vt is the true wind speed and is the heel angle. Using the driving and heeling aerodynamic force Fx and Fy component in the yacht body reference system the corresponding drag and lift forces components can be obtained as follows: Figure 46. Lift coefficient vs apparent wind angle DRAG = Fx cos( AWA) + Fy sin( AWA) (6) Heel effect on sails aerodynamics is outlined in the LIFT = Fx sin( AWA) + Fy cos( AWA) following: in figures 43-44 the measured CD and CL values defined using the effective wind angle and effective wind speed according to eq.(5) are reported for Then the corresponding drag and lift coefficients CD and the 30° heel condition too. CL can be evaluated: 1 DRAG = Va2C D ( AWA) S 2 (7) 1 LIFT = Va2C L ( AWA) S 2 where S is the actual sailplan area. So when the boat heels over the apparent wind angle decreases and the apparent wind speed reduces and this results in a loss of aerodynamic drive force. This approach is very interesting because only one set of sails coefficients can be used to any heel angle. As an example in figures 45-46 the CD and CL measured values at different AWA are reported for the medium roach mainsail+ non overlapping jib in upright condition. Figure 47. MimsG100 drag coefficient At each AWA, values corresponding to each run (i.e. each trim) performed are reported and red full dots correspond to the maximum driving force condition trimming point. Figure 48. MimsG100 lift coefficient Figures 49-50 refer to the medium roach + medium overlapping sailplan where upright, 15° heel and 30° heel Figure 45. Drag coefficient vs apparent wind angle configuration are reported. 23 yacht heel and on the actual apparent wind angle, obtained from an interpolation between the available experimental database. MimsG135 0.8 0.7 0.6 0.5 heel 0 Cx 0.4 heel 15 0.3 heel 30 0.2 0.1 0 0 10 20 30 40 50 Awa [°] Figure 49. MimsG135 drag coefficient Figure 51. MimsG135 driving force coefficient MimsG135 1.6 1.4 1.2 1 heel 0 Cy 0.8 heel 15 0.6 heel 30 0.4 0.2 0 0 10 20 30 40 50 Awa [°] Figure 52. MimsG135 heeling force coefficient Figure 50. MimsG135 lift coefficient As a general comment from the experimental obtained Finally it’s also interesting to mention that results and result it can be seen that CD and CL curves tend to be conclusion of the present paper go exactly in the opposite different with respect to AWA at different heels and direction with respect of results presented in [8]. Despite differences are larger at wider apparent wind angles. that only qualitative results are reported in that paper This trend is confirmed also for all the other sailplan without any details on the sailplan tested available, it’s tested (not reported here for lack of space reasons). author’s opinion that in principle results showing that It should be also noticed that using the so called effective there is no drop-off in driving force over the entire angle approach implies to move to any heel angle on the operational range of the sails until 30° heel are not upright condition coefficients curves, depending on the particularly surprising and can be explained considering effective wind angle, leading to a general lift and drag sails-hull interaction effects. Some wind tunnel tests overestimation at wider angles while at the closer angles recently performed by the authors on a IACC Version 5 this error is going to reduce. yacht model on upwind sails at various heel angles (not The corresponding situation for the abovementioned reported here for confidentiality reasons) reveal that at sailplan in terms of drive and heeling force is outlined in 20° heel the effect of heel was to produce low base drag figures 51-52. compared to other heel and associated higher driving As can be seen at wider apparent wind angle using force but that could be attributed to changes in the upright condition coefficients and effective wind angle windage drag with heel: this moreover offers the both forces are overestimated. prospect of investigating this feature together with hull This could also explain the reason why VPP solutions are shape to reduce windage at different heel angles generally obtained in association with large values of flat Another important point outlined from author’s parameter: in fact depowering introduced by flat values performed tests and affecting aerodynamic forces with sometime less than 0.5-0.6 are not realistic and probably heel was related to the boom height with respect to the due to overestimation of aerodynamic forces in heeled deck: figure 53-54 show the wind velocity vectors conditions. coloured by normalisation to the free stream incoming An approach more consistent with experimental data flow in a vertical transverse plane that cuts the mainsail could be to use CD and CL values, depending on actual at 33% of boom length (from the mast) respectively for 24 upright, 15°heeled and 30° heeled conditions obtained 6. CONCLUSIONS from the abovementioned numerical simulations. This paper gives an overview of the large amount of research activities carried out at Politecnico di Milano Twisted Flow Wind Tunnel in order to investigate the performance of upwind sails in heeled condition. Several rig planform variations in mainsail roach and jib overlap have been tested. Experimental results show that sailplan aerodynamic forces reduce with heeling, that drag and lift coefficients curves are different with respect to apparent wind angle at different heels and differences are larger at wider apparent wind angles. This trend is confirmed for all the sailplan tested and has been clarified with the aid of numerical results obtained using RANS methods performed on the tested sailplan configurations. Experimental results reveal that to the so called “heeled plane approach”, largely used in the standard VPP Figure 53. Velocity vectors in a vertical plane aerodynamic models, leads to a general lift and drag perpendicular to the boom in upright condition overestimation at wider angles while at the closer angles this error is going to reduce. Main conclusion is that with reference to standard applications the so called heeled plane approach is quite adequate even if at upwind wider apparent wind angle both forces are overestimated. Potential improvement of the generally used Kerwin’s assumptions based aerodynamic model, in order to take into account heel effects, are finally outlined based on the available experimental database. References 1. J. M. C. Campbell, & A. R. Claughton – Wind Tunnel Testing of Sailing Yacht Rigs – 13th HISVA symposium – Amsterdam 1994 2. Fossati F. et al., ‘Wind Tunnel Techniques for Investigation and Optimization of Sailing Yachts Figure 54. Velocity vectors in a vertical plane perpendicular to the boom at 15° heel Aerodynamics’, High Performance Yacht Design Conference Auckland, 14-16-Feb. 2006 3. Kerwin, JE “A velocity Prediction Program for Ocean racing yachts”, Rep 78-11 MIT, July 1978 4. Fossati, F.& Zasso, A.& Viola I., “Twisted Flow Wind Tunnel Design for Yacht Aerodynamic Studies”, Proc. of the 4th European and African Conference on Wind Engineering, J. Naprstek & C. Fisher, Prague, 11-15 July, 2005. 5. Fossati F. et al, “Experimental Database of Sails Performance and Flying Shapes in Upwind Conditions” Innov’sail 2008, RINA 29-30 May Lorient, 2008 6. P. S. Jackson, “Modelling the Aerodynamics of Upwind Sails” – Journal of Wind Eng. & Ind. Figure 55. Velocity vectors in a vertical plane Aerodyn., vol. 63 , 1996 perpendicular to the boom at 30° heel 7. P. S. Jackson, “An improved Upwind Sail Model for These figures show that a vortex generated by deck edge which increases with heel, but that doesn’t affect VPPs” – SNAME 15th CSYS, Annapolis, 2001 substantially the flow under the boom: this leads to the 8. Teeters J., “The Story so Far”, SeaHorse Magazine, angle of attack reduction associated to heel increasing the July 2007 main reason in decreasing sailplan developed forces. 25

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